Seminario de Ingeniería Matemática y Computacional

El seminario de Ingeniería Matemática y Computacional reune a investigadores y alumnos del área homónima de la PUC cada miércoles durante el semestre. En un ambiente interdisciplinario, abarca diversos tópicos en el área incluyendo Optimización, Análisis Numérico, Cuantificación de Incertidumbre, Ciencias de Datos y Teoría de la Computación, con una fuerte inclinación a distintas aplicaciones en las más diversas áreas.

2023-01-24
13.30-15:30hrs.
Thomas Capelle. Weights & Biases
Desarrollo colaborativo de modelos de ML: cómo trabajar juntos para obtener mejores resultados
Presencial en Auditorio Edificio San Agustín.
Abstract:

La charla será dictada por Thomas Capelle, Machine Learning engineer de la empresa estadounidense Weights & Biases. Él es responsable de mantener activo y actualizado el repositorio WandB/Examples. Su experiencia es en planificación urbana, optimización combinatoria, economía del transporte y matemáticas aplicadas.

El evento incluirá una competencia de clasificación en Kaggle con premios para las mejores propuestas. Los y las participantes deben llevar sus laptops y deben tener acceso a WandB, Colab y Kaggle.

Inscripción gratuita: https://forms.gle/UVEBVJy3NpQHdYB29

2023-01-16
9.30hrs.
Varios. Instituto de Ingeniería Matemática y Computacional
Escuela de Verano SIAM-PUC
Campus San Joaquín
Abstract:
El Capítulo Estudiantil SIAM-PUC y el Instituto de Ingeniería Matemática y Computacional (IMC) los invitan a asistir en la semana del 16 al 20 de enero a la primera edición de la Escuela de Verano Capitulo SIAM PUC 2023 y al Ciclo de charlas Aniversario de Fourier, el cual se realizará en el Campus San Joaquín UC. Este evento será una instancia para conocer y acercarse al trabajo de profesores del IMC, conocer los temas que se desarrollan en el Magíster en Ingeniería Matemática y Computacional y conmemorar los 200 años de la teoría analítica del Calor de Fourier .

La Escuela está dirigida tanto a estudiantes como académicos/as e investigadores interesados/as en temas de ingeniería matemática y matemáticas aplicadas, y contempla las siguientes actividades:
  • Charlas de académicos de Ingeniería Matemática.
  • Cursos de los temas desarrollados por académicos del IMC.
  • Ciclo de charlas sobre Análisis de Fourier.
  • Coffee break durante los días que dure el evento.
Este evento es GRATUITO con CUPOS LIMITADOS. Formulario de postulación: https://form.jotform.com/223173577317661

Más información: https://sites.google.com/uc.cl/capitulosiampuc/escuela-de-verano
2022-11-28
13hrs.
Gianluca Iaccarino. Stanford University
What is Computational Mathematics and ICME for you?
Presencial en Auditorio Edificio San Agustín.
Abstract:
The Institute for Computational and Mathematical Engineering (ICME) at Stanford University is an interdisciplinary graduate program (granting Masters and PhDs) at the intersection of mathematics, computing, and science and engineering. ICME was established in 2004, is part of Stanford School of Engineering and provides a link between fundamental mathematics/statistical sciences, computer science and engineering applications. In ICME:

We design state-of-the-art mathematical and computational models, methods and algorithms.

We collaborate closely with engineers and scientists in academia and industry to develop improved computational approaches and advance disciplinary fields.

We train students and scholars in mathematical modeling, scientific computing and advanced computational algorithms.

In this talk I will give an overview of ICME, and give examples of recent research activities highlighting ICME students.

Link de inscripción: https://forms.gle/YcQYNVfWvMr4end29
2022-10-19
13hrs.
Carlos Spa. Computer Applications in Science and Engineering (Case) Department, Barcelona Supercomputing Center (Bsc-Cns)
Pseudo-spectral methods in room acoustics simulations
Presencial en Auditorio Edificio San Agustín.
Abstract:
Room acoustics is the science concerned to study the behavior of sound waves in enclosed rooms. The acoustic information of any room, the so-called impulse response, is expressed in terms of the acoustic field as a function of space and time. In general terms, it is nearly impossible to find analytical impulse responses of real rooms. Therefore, in recent years, the use of computers for solving this type of problems has emerged as a proper alternative to calculate these responses. In this talk, we focus on the analysis of the wave-based methods in the time-domain. More concretely, we study in detail the main formulations of Finite-Difference methods, which have been widely used in many room acoustics applications, and the recently proposed Fourier Pseudo-Spectral methods. Both methods are studied and compared in the three different contexts: the wave propagation, the source generation and the locally reacting boundary conditions.
2022-10-14
13hrs.
Clement Lezane. University of Twente
Optimal Algorithms for Stochastic Complementary Composite Minimization
Presencial en Auditorio Edificio San Agustín.
Abstract:
Inspired by regularization techniques in statistics and machine learning, we study complementary composite minimization in the stochastic setting. This problem corresponds to the minimization of the sum of a (weakly) smooth function endowed with a stochastic first-order oracle, and a structured uniformly convex (possibly nonsmooth and non-Lipschitz) regularization term. Despite intensive work on closely related settings, prior to our work no complexity bounds for this problem were known. We close this gap by providing novel excess risk bounds, both in expectation and with high probability. Our algorithms are nearly optimal, which we prove via novel lower complexity bounds for this class of problems. We conclude by providing numerical results comparing our methods to the state of the art.
2022-09-28
13 horas.hrs.
Rodrigo Carrasco. Departamento de Ingeniería Industrial y de Sistemas e Instituto de Ingeniería Matemática y Computacional, Pontificia Universidad Católica de Chile
Energy storage management strategies under uncertain generation: combining prediction and optimization
Presencial en Auditorio Edificio San Agustín.
Abstract:
This work presents a novel approach to scheduling storage units in a photovoltaic generation system based on stochastic optimization. A common approach to take advantage of historical data for stochastic optimization has been to use machine learning techniques to compute relevant scenarios. Instead of this “predict THEN optimize” strategy, we show that using a combined “predict AND optimize” approach results in better recommendations. The resulting scenarios capture the relevant effects on the decision process and not just data features. We show experimental results applied to a real-life control system with limited computation capacity and further validate our results by testing the resulting schedules in an actual prototype.
 

 
 
2022-08-31
13 horas.hrs.
Rodrigo Carrasco. Departamento de Ingeniería Industrial y de Sistemas e Instituto de Ingeniería Matemática y Computacional, Pontificia Universidad Católica de Chile.
Energy storage management strategies under uncertain generation: combining prediction and optimization
Presencial en Auditorio Edificio San Agustín. (Link Zoom disponible escribiendo a imc@uc.cl)
Abstract:

Due to climate change concerns, many governments have pushed for higher penetration of intermittent renewable energy sources. Among these energy sources, photovoltaic (PV) generation is one of the most sought-off, particularly by domiciliary users and small industries. However, the main drawback of this energy source is its variability and intermittency, not being available for the whole day. One way of diminishing this drawback is to use energy storage systems like batteries. In Chile, as in several other countries, the new regulation allows selling excess household generation, albeit at a price significantly lower than the consumer price. With this new setting, the residential sector user, with solar panels installed in their home, can not only use the energy from that source and connect to the electrical distribution network when required. In addition, she can also sell the excess energy generated to the distribution network, getting an economic benefit from this sale. The decision becomes complex when storage capacity, like batteries, is added to the user. In this new case, the decision process must consider when and how much to store or sell to the grid; and whether energy should be used, sent to the network, or stored in the system.

This work presents a novel approach to scheduling these storage units in a PV generation system based on stochastic optimization. A common approach to using historical data for stochastic optimization has been to use machine learning techniques to compute relevant scenarios. Instead of this “predict then optimize” strategy, we show that using a combined “predict and optimize” approach results in better recommendations. The resulting scenarios capture the relevant effects on the decision process and not just data features. We show experimental results applied to a real-life control system with limited computation capacity and further validate our results by testing the resulting schedules in an actual prototype.

This is joint work with Helena García, Tito Homem-de-Mello, Gonzalo Ruz, Francisco Jara, and Carlos Silva. This work was partially funded by FONDEF grant ID19I10158. 

2022-08-24
13 horas.hrs.
Juan Reutter. Departamento de Ciencia de la Computación, Pontificia Universidad Católica de Chile
The power of graph neural networks
Presencial en Auditorio Edificio San Agustín.
Abstract:
The power of Graph Neural Networks (GNNs) is commonly measured in terms of their ability to separate graphs: a GNN is more powerful when it can recognize more graphs as being different. Studying this metric in GNNs helps in understanding the limitations of GNNs for graph learning tasks, but there are few general techniques for doing this, and most results in this direction are geared at specific GNN architectures.
 
In this talk I will review our recent work in studying the separation power of GNNs. Our approach is to view GNNs as expressions specified in procedural languages that describe the computations in the layers of the GNNs, and then analyze these expressions to obtain bounds on the separation power of said GNNs. As we see, this technique gives us an elegant way to easily obtain bounds on the separation power of GNNs in terms of the Weisfeiler-Leman (WL) tests, which have become the yardstick to measure the separation power of GNNs. If time permits, I will also review some of the by-products of our characterization, including connections to logic and approximation results for GNNs. 
2022-08-10
13 horas.hrs.
Nishant Mehta. Department of Computer Science, University of Victoria
Best-case lower bounds in online learning
Vía Zoom
Abstract:
I will begin by introducing an online learning problem motivated by group fairness considerations. It is standard in online learning to prove sublinear upper bounds on the regret, a key performance measure in online learning and online convex optimization. An alternative concept is a best-case lower bound — the largest improvement an algorithm can obtain relative to the single best action in hindsight. Best-case lower bounds have connections to fairness: it is known that best-case lower bounds are instrumental in obtaining algorithms for the popular decision-theoretic online learning (DTOL) setting that satisfy a notion of group fairness. A parallel motivation of this work is to better understand the adaptivity of a learning algorithm; while some algorithms provably exhibit certain types of adaptivity, we show that they are provably prohibited from obtaining another desirable form of adaptivity (related to what is known as the shifting regret). Our contributions are a general method to provide best-case lower bounds in Follow the Regularized Leader (FTRL) algorithms with time-varying regularizers, which we use to show that best-case lower bounds are often of the same order as existing upper regret bounds: this includes situations with a fixed learning rate, decreasing learning rates, and adaptive gradient methods. We also show that the popular linearized version of FTRL can attain negative linear regret and hence does not admit non-trivial best-case lower bounds in general.
 
This is joint work with Cristóbal Guzmán and Ali Mortazavi.

Link Zoom: https://us06web.zoom.us/j/81151863460?pwd=Z0RPTHZKd1hTTndrNHMwMkpJTjZlZz09 (Código: McJ80c)
2022-06-15
13 horas.hrs.
Benjamín Palacios. Departamento de Matemáticas, Pontificia Universidad Católica de Chile
The inverse problem of photoacoustic tomography: theoretical aspects and reconstruction methods
Presencial en Auditorio Edificio San Agustín.
Abstract:
Photoacoustic Tomography (PAT) is a promising hybrid medical imaging modality that is able to generate high-resolution and high-contrast images by exploiting the coupling of electromagnetic pulses (in the visible region) and ultrasound waves via de photoacoustic effect. The mathematical problem splits into two steps, one involving the inversion of boundary acoustic data to determine the initial source of waves, and the second step uses this internal information to retrieve optical properties of the medium and it is commonly known as Quantitative PAT.

In this talk, I will introduce the modality and focus on the ultrasound propagation component which is mathematically modeled as an inverse initial source problem for the wave equation. I will then discuss mathematical aspects of this inverse problem and present some recent theoretical results. The last part of the presentation will be devoted to addressing some open questions related to reconstruction methods and numerical implementations.
2022-06-01
13 horas.hrs.
Cristián Escauriaza. Departamento de Ingeniería Hidráulica y Ambiental, Pontificia Universidad Católica de Chile
Transporte Turbulento en Zonas de Almacenamiento Superficial: Perspectivas Lagrangianas y Eulerianas
Presencial en Auditorio Edificio San Agustín.
Abstract:
Las zonas de almacenamiento superficial en ambientes fluviales y costeros se caracterizan por grandes regiones laterales de recirculación, dominadas por múltiples estructuras coherentes turbulentas que interactúan entre sí y con los bordes. Estos flujos que poseen velocidades más bajas, juegan un papel fundamental en el transporte de contaminantes y de sedimentos, y en la absorción de nutrientes en ríos y en la costa. Sin embargo, la dinámica de las estructuras coherentes en estas zonas es altamente compleja, con múltiples escalas espaciales y temporales. Modelos numéricos de alta resolución que capturan estos flujos a altos números de Reynolds proporcionan información sobre los mecanismos de transporte y los factores que influyen a escalas espaciales más grandes. En este trabajo estudiamos los procesos físicos utilizando simulaciones numéricas de las ecuaciones filtradas de Navier-Stokes junto con ecuaciones de transporte. Implementamos un modelo Lagrangiano de partículas para estudiar tiempos de residencia y realizar análisis estadísticos de trayectorias que permiten comprender los impactos a mayor escala, y sus implicancias en parametrizaciones de transporte.
2022-05-25
13 horas.hrs.
Pablo Barceló. Instituto de Ingeniería Matemática y Computacional, Pontificia Universidad Católica de Chile
The AGM Bound
Presencial en Auditorio Edificio San Agustín.
Abstract:
In several computer science applications one encounters the following problem: Given two edge-labeled graphs G and H, how many homomorphic images of H can be found in G? Atserias, Grohe, and Marx developed a tight bound for this number, denoted #Hom(H,G), which is now known as the AGM bound. The bound relates #Hom(H,G) with the fractional edge covers of H in a very elegant and direct way. We will present a self-contained and simple proof of this result using Holder's inequality.
2022-05-18
13 horas.hrs.
David M. Hernandez. Institute for Theory and Computation, Harvard-Smithsonian Center for Astrophysics
New mathematical tools for calculating gravitational dynamics in planetary systems and other N-body problems
Presencial en Auditorio San Agustín
Abstract:
I describe new mathematical tools I've built to solve different problems in gravitational dynamics. I first describe maps that solve the gravitational system of ordinary differential equations describing asteroids in the Solar System.  Enforcing that these maps be time-reversible and symplectic can significantly improve the reliability of the long-term dynamics of these bodies.

I then tackle the problem of the stability of the Solar System.  Although great progress has been made in the last decades towards an understanding of chaos and stability of the Solar System due to the development of modern computers, I show that important studies are affected by numerical chaos, which causes artificial Solar System chaos and instability.  This numerical instability arises from resonances between the time step and physical Solar System frequencies, and is an inherent property of symplectic maps.  I discuss our current work to calculate Solar System stability, and in particular Mercury's future trajectory, without the effects of numerical chaos.

I next describe a suite of tools, including powerful new Kepler solvers and new symplectic integrators and their tangent equations that are designed to solve for the orbits of planets in exoplanetary systems.  Unlike other popular methods, we can solve planetary systems with arbitrary geometries and orbits including moons.  We have implemented these tools to solve the transit timing variation problem, and derive the properties and possible compositions of TRAPPIST-1 planets.  Some of this work has been incorporated in the popular Rebound code.
2022-05-04
13 horas.hrs.
Christoph Dürr. Centre National de la Recherche Scientifique (Cnrs); Centro de Modelamiento Matemático (Cmm), Universidad de Chile
Three problems under explorable uncertainty
Presencial en Auditorio Edificio San Agustín. Opción vía Zoom: https://us06web.zoom.us/j/88006820878?pwd=aCtnM0QvMlFYK3BjdWU5VWRQbzRXdz09 (Código: MtEQ0c)
Abstract:
If you have ever worked on an industrial project you might have noticed that it is really difficult to obtain the input data for the problem you are supposed to solve. At the best you obtain some estimations. This situation motivated the study of a computational model, where the input is given only in an imprecise form, in the sense that every variable is drawn from a known distribution with finite support. You have the possibility to make queries in order to learn the exact values. The goal is to make as few queries as possible in order to solve the problem. In this talk we will consider the problem of sorting a set of variables, of determining the minimum among a set of variables, and more generally of determining the minimum among several overlapping sets of variables.
 
This talk will cover results from the following papers:

Orienting (hyper)graphs under explorable stochastic uncertainty. Evripidis Bampis, Christoph Dürr, Thomas Erlebach, Murilo S. de Lima, Nicole Megow and Jens Schlöter. European Symposium on Algorithms (ESA), 2021.

Query minimization under stochastic uncertainty. Steven Chaplick, Magnús M. Halldórsson, Murilo S. de Lima and Tigran Tonoyan. Latin American Theoretical Informatics Symposium (LATIN) 2020.
2022-04-27
13 horas.hrs.
Pawel Pralat . Department of Mathematics, Ryerson University and Leader of Fields-Cqam Lab on Computational Methods in Industrial Mathematics, Fields Institute
Applying random graph models in building machine learning algorithms
Presencial en Auditorio Edificio San Agustín. Opción vía Zoom: https://zoom.us/j/91663629580?pwd=b3AyS3VMN3U5c1hVR0ZSY0ZyTHE4dz09 (Código: 442495)
Abstract:
Currently, we experience a rapid growth of research done in the intersection of mining and modelling of complex networks. In this talk I will present a few problems from this intersection and show how random graphs were used to design the tool. There are two main reasons to include random graph models in mining complex networks:

Synthetic models: Many important algorithms (such as community detection algorithms) are unsupervised in nature. Moreover, despite the fact that the research community gets better with exchanging datasets (see, for example, Stanford Large Network Dataset Collection (SNAP)) there are still very few publicly available networks with known underlying structure, the so-called ground truth. Hence, to test, benchmark, and properly tune unsupervised algorithms, one may use random graphs to produce synthetic “playground”: graphs with known ground truth (such as the community structure in the context of community detection algorithms).

Null-models: Null-model is a random object that matches one specific property P of a given object but is otherwise taken, unbiasedly, at random from the family of objects that have property P. As a result, the null-models can be used to test whether a given object exhibits some “surprising” property that is not expected on the basis of chance alone or as an implication of the fact that the object has property P. Applications include community detection, link prediction, and anomaly detection, just to name a few.
2022-04-13
13 horas.hrs.
Augusto Gerolin. Department of Mathematics and Statistics and Department of Chemistry and Biomolecular Sciences, University of Ottawa
Schrödinger Bridges and Sinkhorn algorithm through the lens of Optimal Transport Theory
Zoom: https://zoom.us/j/91663629580?pwd=b3AyS3VMN3U5c1hVR0ZSY0ZyTHE4dz09 (Código: 442495)
Abstract:
In this talk we will give a friendly introduction to the Sinkhorn algorithm (aka Matrix Scaling, Iterative Proportional Fitting Procedure, etc) in the context of optimal transportation theory. We will exploit the equivalence between the Schrödinger Bridge problem and the Shannon entropy penalized optimal transport in order to find a different approach to the duality, in the spirit of optimal transport. In particular, this duality approach extends to more general convex entropy penalizations, provides an alternative proof of the convergence of the Sinkhorn algorithm with two marginals and shows convergence of the Sinkhorn algorithm in the multi-marginal case.  
 
The talk has few prerequisites and no contraindications. Therefore, MSc and PhD students are encouraged to attend as well.
2022-04-06
13 horas.hrs.
Anastasios Matzavinos. Instituto de Ingeniería Matemática y Computacional, Pontificia Universidad Católica de Chile
Data assimilation and uncertainty quantification in molecular dynamics
Zoom: https://zoom.us/j/91663629580?pwd=b3AyS3VMN3U5c1hVR0ZSY0ZyTHE4dz09 (Código: 442495)
Abstract:
A recent approach to Bayesian uncertainty quantification using transitional Markov chain Monte Carlo (TMCMC) is extremely parallelizable and has opened the door to a variety of applications which were previously too computationally intensive to be practical. In this talk, we first explore the machinery required to understand and implement Bayesian uncertainty quantification using TMCMC. We then describe dissipative particle dynamics, a computational particle simulation method which is suitable for modeling extended biomolecular structures, and develop an example simulation of a lipid bilayer membrane in fluid. Finally, we apply the algorithm to a basic model of uncertainty in our lipid simulation, effectively recovering a target set of parameters (along with distributions corresponding to the uncertainty) and demonstrating the practicality of Bayesian uncertainty quantification for complex particle simulations.
2022-03-23
13 horas.hrs.
Jorge Vera. Departamento de Ingeniería Industrial y de Sistemas, Pontificia Universidad Católica de Chile
Optimización para Gestionar la Complejidad en Sistemas de Salud
Presencial en Auditorio Edificio San Agustín (Opción vía Zoom: https://zoom.us/j/91663629580?pwd=b3AyS3VMN3U5c1hVR0ZSY0ZyTHE4dz09 (Código: 442495)
Abstract:
Los sistemas de salud son uno de los mejores ejemplos de sistemas complejos: interacciones entre diversas áreas y grandes incertidumbres. La toma de decisiones sobre recursos, atención de pacientes y otros es un proceso muy difícil y las ineficiencias se traducen en consecuencias negativas para los usuarios, como son, por ejemplo, las largas listas de espera que se observan en muchos lugares. Las herramientas de la Investigación Operacional han contribuido a enfrentar esta complejidad y en esta charla mostraremos algunos desarrollos que buscan abordar problemas de admisión de pacientes en un sistema hospitalario bajo incertidumbre en distintos horizontes de tiempo. Mostraremos un problema de optimización multiobjetivo de 2 etapas bajo incertidumbre, que busca un balance adecuado entre uso de los recursos de camas y el traslado de pacientes a otras unidades hospitalarias. También mostraremos una modelación de las decisiones más detalladas de admisión a distintas áreas de un hospital bajo condiciones de incertidumbre en el tiempo de estadía de los pacientes. Este último problema es abordado mediante Optimización Robusta Distribucional. También discutiremos algunas extensiones.
2022-03-16
13 horas.hrs.
Dieter Mitsche. Instituto de Ingeniería Matemática y Computacional, Pontificia Universidad Católica de Chile
An introduction to hyperbolic random graphs (Introducción a grafos aleatorios hiperbólicos)
Presencial en Auditorio Edificio San Agustín (Para quienes no puedan asistir en persona, el link de Zoom es https://zoom.us/j/91663629580?pwd=b3AyS3VMN3U5c1hVR0ZSY0ZyTHE4dz09, Código: 442495)
Abstract:
About ten years ago, Krioukov et al. proposed a new model for complex networks --- the so-called model of random hyperbolic graphs. By means of maximum likelihood estimation the authors therein observed a very good fit with (a subnetwork of) the Internet router network. This drew the attention of the mathematics community to this model, and by now several aspects are already well understood from a mathematical point of view.

In this talk we first survey typical desired properties of complex networks, and then we introduce formally the model of random hyperbolic graphs. Time permitting we illustrate how to show the desired properties in this model.
2021-12-01
13 horas.hrs.
Mircea Petrache. Departamento de Matemáticas, Pontificia Universidad Católica de Chile
" Lottery ticket hypothesis " : buscando estructuras esenciales de redes neuronales profundas
Auditorio Edificio San Agustín / Zoom: https://zoom.us/j/93835721676?pwd=eXJpck4vazc3MFNsYTZjWHVnZElSdz09
Abstract:
Las redes neuronales profundas permiten extraer información desde conjuntos de datos de larga dimensión, sin conocer a priori la estructura de los datos, pero con costos computacionales a veces muy elevados. "Lottery ticket hypothesis" es la denominación una fenómeno descrito experimentalmente empezando por Frankle-Carbin 2019 (que tiene unas 1500 citas), en base al cual redes largas con muchos parámetros, tienden a tener algunas subredes muy chicas y muy especiales ("papeletas ganadoras" de una lotería), que además son igual de performantes que la red inicial. La pregunta natural de "cómo encontrar la papeleta ganadora", o aun sólo de justificar su existencia y seleccionar propiedades importantes, nos lleva directamente a la tarea de desarrollar nuestro entendimiento sobre la forma geométrica de los datos. Presentaré una introducción informal a las grandes preguntas abiertas en el campo, y unos intentos interesantes de respuesta, que puedan servir como base de partida para trabajar en este campo en crecimiento explosivo. Basado en un grupo de estudio que empezamos junto con Hans Löbel y Felipe Gutiérrez, en el CenIA.